Leave the ice cream out to soften enough to be spreadable.
Add the sandwich cookies to a food processor, process until just crumbs remain.
Add the melted butter, process to combine.
Press into the bottom of a 10-inch springform pan.
In a microwave-safe bowl add the chocolate chips and stout, microwave on high for 30 seconds, stir and repeat until well combined (this can also be done in the top of a double boiler.
Pour half of the mixture in an even layer over the crust. Freeze until set.
Add 1 ½ pints of ice cream over the chocolate, smooth into an even layer.
Add the remaining chocolate mixture, top with mini chocolate peanut butter cups, freeze until set.
Add the remaining ice cream, smooth into an even layer.
Add the heavy cream, powdered sugar, and vanilla extract to the bowl of a stand mixer beat on high until well combined. Smooth over the top of the last ice cream layer. Freeze until ready to serve.
Make the caramel sauce for serving:
Add the sugar, cream of tartar, and water to a large heavy bottom saucepan, stir until the sugar is dissolved, stop stirring.
Boil until a dark amber, about 8 minutes, swirling the pan occasionally if hot spots develop.
Remove from heat, stir in the butter until melted.
Slowly stir in the heavy cream and then the salt.
Allow the cake to sit at room temperature for about ten minutes to soften enough to cut.
Drizzle with caramel before serving.
Notes
*cream of tartar is option but it does prevent crystallization if grainy caramel has ever been an issue for you.